Acquiring contact position parameters and detecting contact of a joint

ABSTRACT

The present invention relates to a data processing method of determining a transformation for the relative positions of two body parts which are connected to each other by a joint, the method comprising the following steps:
         a) acquiring first body part position transformation data comprising first body part position transformation information describing a first body part position transformation for the position of a first body part of the two body parts relative to a first reference structure assigned to the first body part;   b) acquiring second body part position transformation data comprising second body part position transformation information describing a second body part position transformation for the position of a second other body part of the two body parts relative to a second other reference structure assigned to the second body part;   c) acquiring reference structure position transformation data comprising reference structure position transformation information describing a reference structure position transformation for the position of the first reference structure relative to the second reference structure for at least two movement states of the joint;   d) determining, based on the first body part position transformation data and the second body part position transformation data and the reference structure position transformation data, joint position transformation data comprising joint position transformation information describing a joint position transformation for the position of the first body part relative to the second body part for the at least two movement states.

The present invention is directed to a method of determining a transformation between the positions of two body parts in accordance with claim 1 and a corresponding computer program, computer running that program and navigation system comprising such a computer.

When implanting an artificial joint, in particular artificial knee joint, into a patient's body, it is often desirable to determine the range of motion (ROM) of the artificial joint. In particular, determining the range of motion comprises determining possible positions (comprising translations and rotations of the components of the in particular artificial joint relative to one another) which are generally possible while preferably resulting in a desired contact between the components. The information about such contact positions may then serve as a basis for a virtual model of the artificial joint which is in particular used as a basis for simulating the range of motion of the respective patient's body part (in particular, knee joint) after undergoing the implant surgery.

So far, such information about contact positions (contact position transformation information) could only be gathered on the basis of predetermined computer-aided design data about the components of the artificial joint which, however, may deviate from the actual characteristics (in particular, the actual geometry) of the implant components to be used, or which cannot be provided at all, e.g. for implant components that have been worn or for which no data exists.

A problem to be solved by the invention thus is to improve the flexibility and accuracy of determining a range of motion of a joint, in particular an anatomical or artificial joint, in particular of a specific sample anatomical or artificial joint.

This problem is solved by the subject-matter of any appended independent claim. Advantages, advantageous features, advantageous embodiments and advantageous aspects of the present invention are disclosed in the following and contained in the subject-matter of the dependent claims. Different advantageous features can be combined in accordance with the invention as long as technically sensible and feasible. In particular, a feature of one embodiment which has the same or similar function of another feature of another embodiment can be exchanged. In particular, a feature of one embodiment which supplements a further function to another embodiment can be added to the other embodiment.

In a particular application, the first inventive method is used to feed data to a continuous joint model (CJM), which can be used to e.g. calculate continuous implant ROMs. A CJM is a method of determining contact position parameters of a joint connecting two bones as disclosed in the applicant's co-pending patent application PCT/EP2011/072323 having the title “Method of determining contact position parameters of a joint connecting two bones” and the attorney's reference 58420 XX which was filed on Dec. 9, 2011, the entire contents of which being incorporated into this application by reference. The method of determining contact position parameters of a joint connecting two bones is also part of this disclosure and in the following also called “method of determining contact position parameters of a joint connecting the first and second (or two) body parts”.

In the framework of this disclosure the term position parameters refers to a way of describing a six-dimensional position that includes translations and rotations and which is disclosed in the context of the method of determining contact position parameters of a joint connecting two body parts.

The first embodiment of the inventive method is directed to a method, in particular a data processing method, of acquiring contact position parameters of two body parts which are connected to each other by a joint, in particular comprise or constitute the joint. This method is also referred to as kinematic footprint. The body parts may be artificial, i.e. comprise an implant, and thus be connected by an artificial joint. The body parts may, however, also be anatomical, i.e. real or natural, body parts and thus be connected by an anatomical joint.

In the framework of this disclosure, entities (the entity being e.g. a physical structure such as a body part or a medical instrument, in particular a reference structure or a virtual structure such as a plane or point defined in space) are geometrically represented by assigned coordinate systems. A position of an entity is a relative position with respect to a second entity and defined by the pose of its assigned reference system (in particular, a coordinate system) with respect to another reference system (in particular, a coordinate system), that in particular is associated to the second entity. Preferably, the entity of which the relative position is described rests fixed relative to its assigned coordinate system, in particular the coordinate system is centered (i.e. has its origin) in the respective entity. Preferably, the coordinate systems which are assigned to different body parts, are different from one another. In particular, the bases of the coordinate systems are not identical. As becomes clear from the above, the position of the entity, in particular body part, is defined as an absolute position only with respect to its assigned reference system (in particular, coordinate system). Where in the framework of this disclosure a relative position of an entity (e.g. in particular a body part or an instrument) shall be determined, the term relative position refers to the above defined meaning of a relative position towards another entity and its mathematical representation as a pose of its assigned reference system with respect to another reference system. Such a relative position may also be denoted as a pose of an entity (with respect to another entity in the given textual context), a relative position of two entities or a position of the one entity relative to the other entity.

In the framework of this disclosure a pose (or relative position or position of the one entity relative to the other entity) comprises rotations and translations of the reference system of a first entity which transform this reference system into the reference system (in particular coordinate system) of a second other entity. In particular, rotations may apply around dedicated axes, e.g. the x-, y- and/or z-axis or axes in the mediolateral, anterioposterior and/or proximodistal direction or axes in the normal directions of the transverse, sagittal and/or coronal (in particular frontal) planes of the human body or its parts. In particular, translations may apply along same said axes. In particular, the dedicated axes are the axes of the coordinate system of one of the entities. A pose, a relative position or a position of the one entity relative to the other entity is mathematically described as a transformation (see details below).

Preferably, the body parts for which a transformation between their respective reference systems is to be determined are connected to one another by in particular at least one joint (more particularly, an artificial or anatomical joint). This connection may be established by a direct physical contact between the body parts, e.g. by touching each other.

Preferably, first body part position transformation data is acquired which comprises first body part position transformation information. The first body part position transformation information describes in particular a first body part position transformation for the position of the first body part of the two body parts relative to a first reference structure assigned to the first body part. The first reference structure is assigned to the first body part preferably by being mechanically attached to the first body part. This, however, is not necessary as long as the position of the first reference structure relative to the first marker device remains known, in particular fixed, thus constituting an abstract assignment of the first reference structure to the first body part. The first body part in particular comprises or is a component of a joint. In the case of the joint being an artificial knee joint, the first body part preferably comprises or constitutes (is) the femoral component of the artificial knee joint. It is to be noted that the present invention may also be applied to other joints such as a hip joint, in particular artificial hip joint. In that case, the first body part may comprise or constitute (be) the acetabular component of the artificial hip joint. In particular the current position of the first reference structure relative to second reference structure or a global coordinate system (e.g. the coordinate system of a tracking unit) is detectable. Detecting the position may be effected for example by mechanical tracking, in which case the first reference structure comprises for example a mechanical arm of predetermined dimensions which is mechanically fixed to the first body part and whose change in position (in particular movement) relative to a global coordinate system may be tracked by a tracking unit associated with for example a drive unit for driving (in particular, moving) the first body part. Alternatively or additionally, the first reference structure may be tracked by using emission or reflection of electromagnetic waves. In that case, the first reference structure preferably comprises or constitutes a marker which is mechanically attached to the first body part. In particular, the first reference structure has a predetermined, preferably fixed, position relative to the first body part. In case the first reference structure comprises a marker, preferably a plurality, in particular three, such markers are fixed to a marker device in a predetermined, in particular fixed, position relative to one another and relative to the first body part.

It is the function of a marker to be detected by a marker detection device (for example, a camera or an ultrasound receiver), such that its spatial position (i.e. its spatial location and/or alignment) can be ascertained relative to the marker detection device. The detection device is in particular part of a navigation system. The markers can be active markers. An active marker can for example emit electromagnetic radiation and/or waves, wherein said radiation can be in the infrared, visible and/or ultraviolet spectral range. The marker can also however be passive, i.e. can for example reflect electromagnetic radiation in the infrared, visible and/or ultraviolet spectral range. To this end, the marker can be provided with a surface which has corresponding reflective properties. It is also possible for a marker to reflect and/or emit electromagnetic radiation and/or waves in the radio frequency range or at ultrasound wavelengths. A marker preferably has a spherical and/or spheroid shape and can therefore be referred to as a marker sphere; markers can also, however, exhibit a cornered—for example, cubic—shape.

A marker device preferably comprises retroreflective markers which are configured to reflect infrared electromagnetic radiation which is emitted from e.g. a source device of a navigation system and detected e.g. by an infrared camera. Other well-suited tracking technologies besides optical tracking are electromagnetic or ultrasound or mechanical tracking. The body parts with the associated reference structures are preferably brought into a predetermined functional pose and the position of the markers in particular relative to a coordinate system which is specific for the needs of the navigation system are determined. Preferably, a plurality of such measurements are conducted and position parameters are extracted from the measured data which describe the pose of the joint components (e.g. the body parts) in a specific movement state, in particular in a specific rotational angle and preferably also a specific distance of the joint components relative to one another, more particularly in a specific (three-dimensional) rotational angle and preferably a (three-dimensional) distance. From these position parameters, the reference structure position transformation can be determined by way of known linear algebra and acquired by the first inventive method. The measured data may also represent each measured movement state directly as reference structure position transformation.

A marker device can for example be a reference star or a pointer or one or more (individual) markers in a predetermined spatial relationship. A marker device comprises one, two, three or more markers in a predetermined spatial relationship. This predetermined spatial relationship is in particular known to a navigation system and for example stored in a computer of the navigation system.

A “reference star” refers to a device with a number of markers, advantageously three markers, attached to it, wherein the markers are (in particular detachably) attached to the reference star such that they are stationary, thus providing a known (and advantageously fixed) position of the markers relative to each other. The position of the markers relative to each other can be individually different for each reference star used within the framework of a surgical navigation method, in order to enable the corresponding reference star to be identified by a surgical navigation system on the basis of the position of the markers relative to each other. It is therefore also then possible for the objects (for example, instruments and/or parts of a body) to which the reference star is attached to be identified and/or differentiated. In a surgical navigation method, the reference star serves to attach a plurality of markers to an object (for example, a bone or a medical instrument) in order to be able to detect the position of the object (i.e. its spatial location and/or alignment). Such a reference star in particular comprises a way of being attached to the object (for example, a clamp and/or a thread) and/or a holding element which ensures a distance between the markers and the object (in particular in order to assist the visibility of the markers to a marker detection device) and/or marker holders which are mechanically connected to the holding element and which the markers can be attached to.

Within the framework of this invention, any information about positions of body parts may alternatively or additionally be derived from medical image data contained in images of the respective body parts. In such a case, it is not necessary to attach a marker to the body parts in order to determine the position of a body part. The medical image data is generated for example by applying imaging methods such as conventional x-ray, computed x-ray tomography (CT) or magnetic resonance imaging (MRI; in particular, computed magnetic resonance tomography—MRT) to the body part. In particular, the invention does not comprise or encompass an invasive step representing a substantial physical intervention on the (human or animal) body (as will be explained further down) in connection with determining the position of a body part.

Within the framework of this disclosure, transformations such as e.g. the first body part position transformation in particular are calculation rules, more particularly coordinate transformations, which are represented by preferably an affine transformation. Such an affine transformation is in particular embodied by a (homogeneous) transformation matrix which is preferably invertible and transforms coordinates in a first coordinate system, e.g. the xyz-coordinates of a point of the first body part which is defined in a first body part coordinate system (resting relative to the first body part), into coordinates of the point in a second other, in particular different, coordinate system, e.g. in a first reference structure coordinate system (resting relative to the first reference structure). In particular, the transformations in the disclosure of this framework are rigid-body-transformations and comprise and represent only basic (elementary) rotations around dedicated axes of a coordinate system (e.g. a basic rotation around the x-axis or the y- or z-axis) and translations along dedicated axes (e.g. along the x-axis) or sequences hereof (a sequence of basic rotations and translations) and can thus be decomposed into such translations and basic rotations represented mathematically by transformation matrices. In particular, the positions of the respective entities are mapped between the coordinate systems. To this end, the transformations, e.g. the first body part position transformation, may comprise or consist of a basis transformation, in particular a transformation of the first body part coordinate system into a common basis coordinate system, and another basis transformation of the reference structure coordinate system into the same common basis coordinate system, that basis coordinate system then having a basis which is common for the first body part and the first reference structure and in which the relative position of the first body part and the position of the first reference structure can be calculated as resulting transformation matrix by multiplying the transformation matrices of the two basis transformations.

Preferably, second body part position transformation data is acquired which comprises second body part position transformation information. The second body part position transformation information in particular describes a second body part position transformation for the position of a second other body part of the two body parts (i.e. a second body part other than or different from the first body part) relative to a second other reference structure (i.e. a second reference structure other than or different from the first reference structure) associated with the second body part. In case the joint is an artificial knee joint, the second body part preferably comprises or constitutes (is) the tibia component of the artificial knee joint. In case the artificial joint is an artificial hip joint, the second body part preferably comprises or constitutes (is) the femoral neck or femoral head component of the artificial hip joint. The second reference structure can be described in analogy to the first reference structure, a detailed description of the second reference structure therefore is omitted here. Likewise, the second reference structure can be assigned to the second body part just as the first reference structure can be assigned to the first body part, a detailed description of the second reference structure therefore is also omitted. The second body part position transformation is a transformation (of coordinates) from the coordinate system of the second body part into (coordinates in) the coordinate system of the second reference structure in analogy to the way the first body part position transformation is a transformation (of coordinates) from the coordinate system of the first body part into (coordinates in) the coordinate system of the first reference structure.

Preferably, reference structure position information data is acquired which comprises reference structure position transformation information. The reference structure position transformation information in particular describes a reference structure position transformation for the position of the first reference structure relative to the second reference structure. A reference structure position transformation is acquired preferably for each of a plurality of movement states, in particular for at least two movement states, of the joint.

A movement state of the joint is understood to describe a kinematic state of the joint and encompass in particular both a (stationary) pose and a state of continuous movement of the joint. A functional movement state of the joint is understood as a particular movement state that encompasses a functional pose. A functional pose of the joint, in particular of the two body parts connected by the joint, encompasses the position of the two body parts relative to one another (as already defined the term position comprises also their rotation or rotational orientation). A functional pose is in particular understood as defining the contact position. The contact position is the mentioned position of the body parts relative to one another while being in contact (the term of contact being defined below).

A basic (elementary) rotation (in particular, three-dimensional basic (elementary) rotation) is in particular defined by an angle which is enclosed by the axes of the coordinate systems being transformed into each other by the basic rotation. The axes of a coordinate system may be aligned to the proximodistal or anteriorposterior or mediolateral direction or to the normal directions of the sagittal and/or transverse and/or frontal planes. The defining angle may for example be a flexion angle and rotate around the axis in mediolateral direction. Preferably, three such angles in particular in the basic movement directions of the joints, in particular of a knee joint, which characterize a range of motion are used for defining the movement states. A sequence of basic rotations that apply these angles one after another can be mathematically implemented as a sequence of homogeneous basic rotation matrices that can be multiplied to form an affine transformation representing the overall result of the sequence of rotations as pose of the movement state. In the case of the joint being a knee, these angles preferably are the internal/external rotation angle, the varus/valgus angle and the flexion/extension angle. For other joints in the human body, such as an ankle joint or a hip joint, corresponding angular directions of movement may be defined. The position of the first body part relative to the second body part is preferably furthermore defined by the translations between the origins of the coordinate systems of the body parts relative to one another along the coordinate systems axes, in the case of the joint being a knee by shifts in the mediolateral, anterioposterior and proximodistal direction, which in particular define a distance between the coordinate systems of the first and second body parts. Corresponding translations (or shifts) may be defined for other joints in the human body such as an ankle joint or a hip joint represented by the joint.

Within the framework of this disclosure, the term of range of motion describes the freedom of the joint to move. In particular, such a freedom to move is defined by a set of movement states of the joint in which there is no mechanical blockage or interlock of the joint which prohibits the joint from taking on the respective movement state. In particular, the range of motion constitutes a set of all the possible movement states of the joint, in particular such movement states which are possible in view of mechanical limitations. Furthermore, the movement states included in the range of motion preferably are functional movement states in which the predetermined contact of the first and second body parts is established and/or maintained.

Preferably, the first and second reference structures are tracked while the joint is being lead through a plurality of, in particular at least two, movement states in order to determine the reference structure position transformation for each of the movement states. The movement of the first body part relative to the second body part (i.e. the movement of the joint) through the plurality of movement state comprises moving (in particular, actively moving) at least one of the first and second body parts either manually or by a driving unit (in particular, an electric motor operatively coupled to a movement device, e.g. a frame to which the first and/or second body parts are attached, in particular mechanically fixed). Preferably, the first body part and the second body part are in physical contact with one another in each of the movement states, preferably functional movement states. Further preferably, such contact is enforced in each of the movement states in particular by in particular at least one of manual or machine-driven pressure exerted on at least one of the first and second body parts.

For example, a manual procedure starts with moving the joint components from a dedicated movement state, in particular a functional movement state. They are being tracked throughout the movements and reference structure position information data is acquired and fed into a computer system for processing. The acquired joint's range of motion (ROM) contains a sequence of functional movement states with their encompassed functional joint poses.

The variation of the movement states, in particular functional movement states, is achieved by an operator who shifts and rotates the components with respect to each other systematically to cover a wide range of motion with all functional poses of the joint. In the example of an artificial knee joint, the femur component would be rotated and translated with respect to the tibia component or vice versa. Preferably, the operator varies position parameters systematically. Further preferably, he will get feedback from the system about covered, uncovered and close movement states in a grid of all functional poses to be acquired. For a first run, he would most conveniently adjust the flexion (flex) and the internal/external rotation (ie) to some value (e.g. flex=0, ie=0) and keep them fixed while shifting the femur implant in anterioposterior (ap) and mediolateral (ml) direction across the tibia implant's surface.

The inventive method preferably comprises only steps of data processing. If necessary, the inventive method may also comprise steps of moving the body parts. However, the inventive method (in particular, any step relating to moving the body parts) does not comprise or encompass an invasive step representing a substantial physical intervention on the (human or animal) body which requires professional medical expertise to be carried out and which entails a substantial health risk even when carried out with the required professional care and expertise. Leading the body parts through the plurality of movement states preferably takes place in a pre-operative state of the joint, i.e. before the artificial joint is implanted into a patient's body. The term of pre-operative state denotes a state of the first body part and/or the second body part (more generally, of the joint connecting the first and second body parts) before surgery is conducted. The method may also be executed irrespective of whether a surgical procedure is envisaged following execution of the inventive method. In particular, the inventive method does not necessitate execution of a surgical method after execution of the inventive method has finished.

Preferably, joint position transformation data is determined based on the first body part position transformation data and the second body part transformation data and the reference structure position transformation data. The joint position transformation data in particular comprises joint position transformation information which in particular describes a joint position transformation for the position of the first body part relative to the position of the second body part for at least a subset of the plurality of movement states through which the joint is (has been) lead and for which the positions of the first reference structure and the second reference structure relative to a global coordinate system (e.g. the coordinate system of the tracking unit) have been determined. Thus, a transformation for the position of the first body part relative to the second body part is determined in particular by matrix multiplication of the matrices describing the first body part position transformation, the second body part position transformation and the reference structure position transformation in the applicable order. The joint position transformation is determined for at least a subset of the plurality of movement states, i.e. for all of the movement states or for fewer than all of the movement states, however for at least in particular two of the movement states.

Preferably, contact position transformation data is determined. The contact position transformation data comprises contact position transformation information. The contact position transformation information comprises a joint position transformation that represents a contact position transformation of the first and second body parts. A contact position transformation is understood to encompass in particular a position of the first and second body parts in which they have or are considered to have (in particular, actually have) in particular a predetermined, more particularly a desired, (direct or indirect) physical contact with one another, in particular by touching one another at preferably predetermined locations (contact locations) on in particular their surfaces. In particular, the predetermined contact describes that the at least two physical structures (namely, at least the first and second body parts) touch each other but do not intersect each other in two- or three-dimensional space. Preferably, the physical structures (the at least first and second body parts) touch each other at two discrete and different locations on each of their surfaces (i.e. at two different points in space) as described below with reference to the method of determining contact position parameters of a joint connecting two bones. Since the first and second body parts are considered to be constituents of a joint, a predetermined contact of the first and second body parts with one another support correct functioning of the joint in particular by proper transfer of forces between the first and second body parts.

Preferably, position parameter grid data is acquired which comprises position parameter grid information. The position parameter grid information in particular describes a grid of the position parameters for at least four degrees of freedom, wherein the nodes of the grid represent independent translations and/or independent rotations of the joint position transformation and are preferably defined by the node datasets of the “Continuous Joint Model” (abbreviated as CJM) which is explained in a later section in the context of the method of determining contact position parameters of a joint connecting two body parts. In the context of the first inventive method, a node represents a movement state, in particular a functional movement state.

The grid preferably is a four-dimensional grid having axes describing numeric values of the anterioposterior shift ap, the mediolateral shift ml and the internal-external rotation ie and the flexion angle fe. Thus, each entry (in particular, node) of the grid is defined for four degrees of freedom. Further preferably, node assignment condition data is acquired which comprises node assignment condition information. The node assignment condition information describes at least one condition for in particular a distance between in particular the values of a set of four position parameters (in particular ap, ml, ie, fe) and a node of the grid, which condition is to be fulfilled for assigning the values of the four position parameters (in particular ap, ml, ie, fe) and the free position parameters (in particular, pd and vv) to that node. The node assignment condition can be extended towards additional conditions in particular a minimum or maximum value to be fulfilled by the free parameters, which condition is to be fulfilled for assigning the values of the four position parameters (in particular ap, ml, ie, fe) and the free position parameters (in particular, pd and vv) to that node. The position parameters preferably are the parameters described in the context of the method of determining contact position parameters of a joint connecting two body parts. The nodes preferably are the nodes described by the node datasets mentioned in the context of the method of determining contact position parameters of a joint connecting two body parts. In particular, each node of the grid is equal to a contact position in which contact between the first and second body parts is established in particular while leading the artificial joint through the plurality of movement states. The pressure exerted during the manual or driven movement ensures that the first and second body parts remain in a contact position while moving them. The contact positions attained thereby are therefore also called ensured contact positions in the sense that contact is enforced and ensured by manual or machine-driven pressure. Therefore, the values of the preferably two free position parameters which make the set of parameters describing a contact position complete, are also assigned to the node. In summary, parameter values for six degrees of freedom are assigned to each node. The condition for the distance preferably is a maximum distance of the value of the set of four position parameters (in particular ap, ml, ie, fe) and a node of the grid. The distance is preferably calculated based on a Minkowski distance function. If a distance to a node is below a predetermined limit, the values of the preferably two free position parameters are assigned to that node. If the node is approached in closer distance at another time during the variation of the functional movement states, the values of the preferably two free position parameters are adjusted to the new values.

Preferably, guidance data comprising guidance information is output to an operator which describes a desired direction of movement of the first and second body parts relative to one another for the manual or driven movement. The guidance data or guidance information is determined based on preferably the already collected contact position transformation data that is assigned to the nodes and the joint position transformation data of the currently attained and tracked movement state. During the acquisition process, the operator is supported to hit all required poses in an efficient way. The computer system will aid him in the acquisition by systematically varying the target values (i.e. for flex and ie) for the next run, showing the deviation to target values (ie, flex) during each run, showing uncovered nodes (compliant in ie and flex) close to the current pose, showing regions of poor coverage during each run. A systematic variation and display of the target values for dedicated parameters, e.g. flex and ie, helps the operator to adjust the current pose accordingly and reach high coverage in each run. In order to keep him on track, the deviation to the target values is also shown. The distance of the current pose of the two body parts (e.g. the femur and the tibia component) to close uncovered nodes is shown to help the operator approaching yet uncovered nodes. In particular, the distance may be decomposed into components in ap and ml direction. Areas of poor coverage are indicated to the operator to guide him to these areas. Most checks will be based on the parameters extracted from the current pose.

If it is determined that the determined position parameter does not fulfill the at least one condition for being assigned to any node, the movement state of the joint in which the position parameter was determined is not assigned to any node. A node of the grid which have no assigned position parameters is considered to represent a void movement state. A void movement state is understood to be an inadmissible movement state in which no contact position may be achieved or in which no contact position exists at all or can't be acquired or in which only an impossible contact position exists or may be achieved, that does not comply with the definition of a predetermined, in particular desired contact position. An example of a void movement state would be a movement state in which no combination of proximodistal translation and varus-valgus rotation between the first and second body parts can be defined to establish a two-point contact between the first and second body parts. An example is a femur joint component that has been moved far beyond the physical borders of the tibial component in anterioposterior direction so that establishing contact is impossible by adjusting proximodistal distance and/or varus-valgus rotation between the components.

In the human anatomy, two bones are typically connected via a joint which exhibits certain kinematic properties. The kinematic properties define a range of motion between the two first and second body parts (in the following also simply called body parts). In other words, the joint typically supports a range of relative positions between the body parts. Such a relative position usually is a contact position in which the surfaces of the body parts are in contact with each other. In particular, there are two or three points of contact or a line contact between the two bones. In general, each contact position is defined by six parameters, wherein three parameters define a translational shift in three dimensions which are typically pairwise orthogonal. In a preferred example, the directions of the shifts are the proximodistal (pd) direction, the anterioposterior (ap) direction and the mediolateral (ml) direction. The other three parameters define a rotational shift or angular alignment, preferably about three pairwise orthogonal axes. Preferably, the three rotational parameters relate to the flexion/extension angle (fe or flex), the internal/external angle (ie) and the varus/valgus angle (vv). In particular, the six parameters of a contact position describe the relative position between a first coordinate system of the first body part and a second coordinate system of the second body part. The relative position is determined based on the joint position transformation data/information and/or the positional measurements for the first and second reference structures.

There are certain desired applications which require the six parameters of a contact position when a subset of the parameters of the contact position is given. An exemplary application is the visualization of the range of motion of the joint. Therefore, a need arises to provide a method for determining the six parameters of a contact position of a joint which connects two body parts, wherein the method in particular should be computationally efficient in order to allow a real-time or on-the-fly determination.

Such a method of determining contact position parameters of a joint has been referenced above as CJM and it is connected to the first inventive method in the way, that the first inventive method is used to establish a database of sample contact position datasets that will be processed in the method of determining contact position parameters of a joint.

The method of determining contact position parameters of a joint connecting two body parts relates to a data processing method for determining six parameters of a contact position of a joint which connects two body parts. One step of the method is acquiring a plurality of sample contact position datasets, wherein each dataset comprises six parameters. These six parameters of the sample contact position datasets correspond to the six parameters describing the contact position. The sample contact position datasets, also referred to as node datasets, represent known and ensured contact positions of the first and second body parts via the joint.

The method of determining contact position parameters of a joint connecting the first and second body parts further comprises the step of acquiring a subset of n of the parameters of the contact position as an input parameter dataset. In other words, n of the parameters of the contact position are predetermined, while the remaining (free) parameters of the contact position (also called free position parameters) have to be determined. The variable n is an integer in the range of 1 to 5, preferably in the range of 3 to 5, and more preferably n has the value of 4.

Other steps of the method of determining contact position parameters of a joint connecting the first and second body parts are selecting at least two of the sample contact position datasets or of a subset of the sample contact position datasets based on the input parameter dataset and determining the m=6-n remaining parameters of the contact position based on the at least two selected sample contact position datasets. In other words, the input parameter dataset is used to select two or more appropriate sample contact position datasets from which the remaining parameters of the contact position are calculated.

Such a model of contact position parameters is also termed “continuous joint model (CJM)”.

With this approach, a database of sample contact position datasets representing discrete sample contact positions of the joint is used as a basis for calculating the six parameters of any (intermediate) contact position. Since the method of determining contact position parameters of a joint connecting the first and second body parts does not use a computationally expensive model, such as a collision detection model, to determine the remaining parameters, but approximates the remaining parameters from (surrounding) sample contact positions, the determination is considerably fast.

Preferably, the remaining parameters are determined by interpolation or extrapolation. In particular, interpolation is preferably applied if all n parameters of the input parameter dataset are lying between the corresponding n parameters of the selected sample contact position datasets. Extrapolation is preferably applied if at least one of the n parameters of the input parameter dataset is lying beyond the corresponding parameters of the selected sample contact position datasets.

The selected sample contact position datasets must be suitable for determining the remaining parameters of the contact position. Preferably, the selected sample contact position datasets correspond to sample contact positions which are, regarding the n input parameters, the nearest neighbours of the contact position. In other words, the criterion for selecting a sample contact position dataset is the distance between the n parameters of the input parameter dataset and the corresponding parameters of a sample contact position dataset. Nearest neighbours of the contact position thus are sample contact positions with a minimum distance to the contact position, wherein the distance is defined by the n input parameters and the corresponding parameters of a sample contact position. A maximum distance between the input parameters of the contact position and the corresponding parameters of the sample contact positions can be defined, wherein sample contact positions with a larger distance cannot be selected. Further, a minimum number of sample contact positions to be selected can be defined.

In one embodiment, the distance between the contact position and a sample contact position is calculated using a Minkowski distance function. For n parameters, the p-norm distance is therefore given by the expression

$\left( {\sum\limits_{i = 1}^{n}{{x_{i} - y_{i}}}^{p}} \right)^{1/p}$

with p≧1. The variable x represents the contact position, the variable y represents a sample contact position and i is an index for the input parameters.

In general, any suitable approach can be used for the interpolation or the extrapolation. However, preferred types of interpolation are a spline interpolation or an interpolation using inverse distance weighting. Spline interpolation in particular refers to a third degree spline interpolation, but also encompasses any other grades as well as B-splines or Bezier curves.

Inverse distance weighting is simple in implementation and can easily be applied to irregularly distributed data. An example for inverse distance weighting is given by the formula

${u(x)} = {\sum\limits_{i = 0}^{S}\frac{{w_{i}(x)}u_{i}}{\sum\limits_{j = 0}^{S}{w_{j}(x)}}}$

with

${w_{i}(x)} = {\frac{1}{{d\left( {x,x_{i}} \right)}^{p}}.}$

In this formula, u is the parameter value to be determined at the contact position x. It is calculated based on S neighbours. The values of the corresponding parameter in the selected S neighbours are given by u_(i) with i running from 1 to S. The variable d describes the distance, regarding the n input parameters, between a neighbour x_(i) and the contact position x. The variable w is a weighting factor or weight which depends on the distance d. The parameter p is a positive real number shaping the interpolation characteristics.

In one embodiment, the sample contact position datasets are arranged in an n-dimensional array and each array entry comprises the m remaining parameters. With this organizational data structure, the selection of the at least two sample contact position datasets is easy and computationally effective, in particular if the sample contact positions are arranged at equidistant intervals. This means that the values of one particular parameter of the sample contact position, and in particular of all n parameters of the sample contact position which are used as input parameters, can assume discrete values, wherein the discrete values have an equidistant distance.

With sample contact positions at equidistant intervals, the selection of two or more sample contact position datasets is computationally efficient, in particular if the index in a dimension of the array corresponds to a multiple of the equidistant interval. If, for example, the interval for an angle is 5 degrees, then an index of 0 corresponds to 0 degrees, an index of 1 corresponds to 5 degrees, an index of 2 corresponds to 10 degrees, and so on. As an option, an offset is added to the index in order to represent shifts symmetrically arranged around a zero shift. So if an angle as one parameter of the contact position is given in 5 degree increments and the index i in the corresponding dimension of the array runs from 0 to 71, then the angle corresponding to an index i is given by i×5 degrees−175 degrees. In a reverse manner, the array index of a sample contact position can be calculated from a particular angle.

In another embodiment, the sample contact position datasets are stored as lists of six parameters each. For example, the six parameters are consecutively written in a line of a text and each line of the text constitutes a sample contact position dataset. With this approach, the parameters of the contact position which form the input parameters can easily be adapted to the desired application in which the method of determining contact position parameters of a joint connecting two bones is used. For example, in one application the remaining parameters are two angles, such as flexion/extension and varus/valgus, while in another application the remaining parameters are all translational shift parameters. Of course, any combination of translational and rotational parameters can constitute the remaining parameters.

In one embodiment, a sample contact position dataset is void for an impossible joint contact position (also called impossible contact position). An impossible joint contact position is a contact position which cannot be assumed by the joint, in particular because it would lie outside the range of motion of the joint. For example, a sample contact position dataset can be made void by assigning a particular value to one of the parameters. In one exemplary implementation, a value outside of the possible range of 360 degrees is assigned to a parameter corresponding to an angle. Since an angle can only lie within a 360 degree range, a value outside this range can be used to indicate a void dataset.

In another embodiment, a sample contact position dataset further comprises affiliate information, also referred to as label, which indicates that the sample contact position belongs to a contact profile of contact positions. A contact profile of contact positions represents for example a particular movement, such as for walking or standing up regarding a knee joint. A contact profile consists of a sequence of contact positions. Preferably, an additional parameter further defines the position of the sample contact position within the sequence of contact positions, i.e. the sequence number.

The labels enable filtering of the sample contact position datasets. In one embodiment, neighbours for interpolating or extrapolating are only selected from sample contact position datasets which have a predetermined label, in particular a label corresponding to a contact profile. Sample contact positions with a particular label may be used as nodes for finer subdivision of the path between them.

Affiliate information can further comprise a 4×4 matrix which describes the spatial transformation from one bone, or implant, to the other(s).

In another embodiment, the step of determining the m=6-n remaining parameters of the contact position is repeated for a sequence of input parameter datasets, which is also referred to as a parameter profile, thus resulting in a sequence of contact positions. The parameter profile preferably corresponds to a contact profile, which means that it might represent a particular movement. With this embodiment, the properties of the joint can be determined for a particular sequence of input parameters for analysis. For example, the properties of the joint can be displayed graphically, for example by plotting the remaining parameters as curves over the variation of the input parameters. In addition, the bones connected by the joint can be displayed in an animation representing the sequence of input parameter datasets.

One aspect of the method of determining contact position parameters of a joint connecting the first and second body parts relates to the acquisition of a sample contact position dataset. In one embodiment, a sample contact position dataset is determined by virtually positioning three-dimensional images of the two bones in a computer such that they are in contact. This might be done using a CAD software provided with a 3D representation of the two body parts. In the software, the relative position of the two body parts is modified until they are in contact. This relative position of the body parts thus positioned is then used as a sample contact position. In a particular embodiment, the relative position between the two body parts is adjusted manually, for example using an input device such as a mouse, a joystick, a trackball, a pointer or a touch screen. The capabilities of the CAD software can be used in order to determine whether or not the two body parts are in contact. The software can for example display a cross-sectional view or a perspective which could not be assumed in the real world, for example from within one of the bones or a cavity of one of the body parts.

As an option, a sample position dataset is automatically determined by using collision detection of three-dimensional models of the first and second body parts.

The first embodiment of the inventive method of acquiring contact position parameters of two body parts which are connected to each other by a joint (also referred to as kinematic footprint) disclosed so far is a way to determine sample position datasets and is applicable without the provision of three-dimensional models or the use of collision detection methods.

The method of determining contact position parameters of a joint connecting two body parts may be combined with the aforementioned features of the first embodiment of the inventive method and/or the features of the second embodiment of the inventive method disclosed in the following without prejudice. In particular, the aforementioned features of the first embodiment of the inventive method may serve to provide input data to the method of determining contact position parameters of a joint connecting two body parts (and lead to a resulting continuous joint model). However, the aforementioned features may also be considered to form a method of its own which in particular does not require the features described in the following for its implementation. It is noted also, that the following features of the second embodiment of the inventive method may also be considered to form a method of its own which in particular does not require the aforementioned features for its implementation.

When implanting an artificial joint, in particular artificial knee joint, into a patient's body, it is often desirable to verify the contact of the components of the joint over a dedicated postoperative range of motion of the artificial joint. Due to the influence of tendons and ligaments the movement states of a joint will most likely deviate from those of the artificial components being inserted. This is why not all possible functional movement states of the components may be part of the postoperative range of motion and other-nonfunctional-movement states may be experienced instead. In particular, verifying contact over a postoperative range of motion comprises verifying contact for each of the movement states that are part of the postoperative range of motion. The information about the contact condition for these movement states may then serve as a basis for judging the quality of the undergone implant surgery or for making decisions on changing or adjusting the implant components.

So far, information about the contact condition (contact condition information) of particular movement states could only be gathered on the basis of the surgeon leading the joint through a postoperative range of motion and determining based on his tactile sensations, whether the implant components are in the desired contact for each particular movement state. He was so far supported by a prior-art navigation system, that calculated contact locations for each pose based on a simplified kinematic model of the joint components and visualized the contact locations (implant contact points) on-screen. The surgeon would try to judge the quality of the contact based on the locations which were marked and displayed with computer graphics on a rendered contact surface of the tibia component for each movement state being tracked.

A problem to be solved in this approach is that due to the high degree of simplification applied, the contact locations calculated by the prior-art navigation system were not determined precisely enough and that contact locations would also be calculated and displayed for movement states not representing a desired contact of the components. In such poses, the components would have no contact or only one-point contact and the navigation system was not able to detect this condition.

This problem is solved by the following features of the second embodiment of the inventive method which are directed to detecting contact between components of a joint (also referred to as contact detection method)—applicable both for artificial (implant) or anatomical joints. Their purpose is to detect a contact condition from the pose of the movement states of the components in a range of motion, in particular in a post-operative range of motion. The second inventive method is directed to distinguish between the conditions of contact, in particular desired contact, on the one hand and no-contact on the other.

There are several applications for such an inventive method of contact detection. In a particular first example application, the joint components are tracked during a postoperative range of motion (ROM) by a navigation system in order to establish the transformation between the components. The contact detection method is conducted on-line for each pose taken. The contact status established with the method can indicate critical situations to the operator. For example, poses being influenced by strong ligament tension or being off typical functional limits may have instable one-point contact, because the implant components lift-off at the second contact point or contact is lost completely. This can be indicated to the user once the contact status is derived with the method of contact detection.

In a particular second example application, the contact detection method improves the above mentioned, currently used calculation technique for implant contact points being used in state-of-the-art navigation systems for the postoperative range of motion. The said calculation technique has weaknesses in detecting lift-off of the components or detecting that the components have moved across their partner component's physical borders (see details and explanations further below). The second inventive embodiment of the inventive method (contact detection method) helps to overcome these weaknesses by indicating such conditions and by masking out wrongly calculated points which occur for lifted-off components and for components moved across their partner component's physical borders. The contact detection method indicates by a contact condition information, whether a contact, in particular a desired contact is established, and this information can be used to mask wrongly calculated points from being displayed.

The contact condition information is preferably determined by making use of a method of determining contact position parameters of a joint connecting two bones as disclosed in the applicant's co-pending patent application PCT/EP2011/072323 having the title “Method of determining contact position parameters of a joint connecting two bones” and the attorney's reference 58420 XX which was filed on Dec. 9, 2011, the entire contents of which being incorporated into this application by reference. The second embodiment of the inventive method disclosed in the following exploits the CJM to detect contact and no-contact without time consuming collision detection techniques that would require high computational effort and can only be applied when virtual three-dimensional models, e.g. CAD-models, of the components exist and are provided. On the contrary, in order to achieve fast and on-line contact detection without the necessity of providing virtual three-dimensional models, e.g. CAD-models, techniques involving collision detection are avoided. A continuous joint model (CJM) is used instead to calculate the joint behavior.

The post-operative range of motion of the joint is acquired for example based on medical image data or position data acquired by an imaging apparatus or a navigation system in a post-operative state of the joint. The medical image or the position data preferably describes a series or sequence of specific movement states, in particular specific poses, of the joint and its bones.

The second embodiment of the inventive method can also be applied to anatomical joints and their body parts (e.g. the femoral condyles and the tibial plateaus) in an analog way. Since there are surgical procedures (e.g. tibial or femoral osteotomies) that change the position of these body parts with regard to their bones (femur and tibia), the joint formed by the body parts keeps its kinematic footprint though the positions of the body parts relative to the bones have been changed. Their postoperative contact condition can thus be detected with the same means and applications as proposed above for artificial joint components.

Preferably, the first and second reference structures are tracked while the joint is being lead through a plurality of, in particular at least two, movement states in order to determine their respective position in a global coordinate system and determine the reference structure position transformation for each of the movement states. The movement of the first body part relative to the second body part (i.e. the movement of the artificial joint) through the plurality of movement state comprises moving (in particular, actively moving) at least one of the first and second body parts manually. The first body part and the second body part do not necessarily have to be in physical contact with one another in any of the movement states. Contact is no prerequisite but it is the task to detect it.

Preferably, contact condition data comprising contact condition information is determined based on the joint position transformation data. The contact condition information in particular describes whether the joint position transformation is a contact position transformation and thus represents a position of the first and second body parts which is a contact position or is close to a contact position of the first and second body parts. In case the position a contact position or close to a contact position, this contact condition is indicated by the contact condition information. In this case the joint position transformation is close to a functional pose and the associated movement state is classified to be or to be close to a functional movement state.

Preferably, the contact condition information is determined based on acquiring a data set comprising six parameters describing joint position transformation information, decomposing the joint position transformation based on acquiring a subset of n of the parameters in the data set as an input parameter data set, n being an integer in the range of 1 to 5 (preferably, n=2) describing the number of predetermined parameters, determining modelled 6-n free parameters of the joint position transformation information and determining a model joint position transformation based on changing the joint position transformation information according to the modelled 6-n free parameters, and wherein preferably a resulting pose of the first and second body parts is determined based on the sample contact position datasets.

Preferably, the contact condition information is further determined based on determining whether a deviation of measured values for the 6-n free parameters is within a predetermined limit from the values of the model 6-n free parameters and determining that the joint position transformation describes a contact position of the first and second body parts if the deviation is within the predetermined limit. The measured values for the 6-n free parameters in particular are the values obtained by decomposing the matrix describing the joint position transformation which has been determined based on the first body part position transformation data, the second body part position transformation data and the reference structure position transformation data. The limit is preferably predetermined individually for each one of the free parameters. However, it is also within the scope of the invention to use a combined limit for the entirety of free parameters. For example, each individual deviation of a model value for a modeled free parameter may be combined with the individual deviations of the other model values for the other modeled free parameters, for example by calculating an average deviation limit or a limit based on a sum of squares of the individual deviations. In this manner, it appears possible to account for an influence which an individual deviation might have on another individual deviation.

The features of the second embodiment of the inventive method of contact detection offer the advantage, that the contact condition is controlled very simply by specifying deviation limits. These limits can be used to compensate for tracking or other inaccuracies, which would otherwise be more difficult to integrate e.g. when using collision detection techniques.

The method in accordance with the invention is in particular a data processing method. The data processing method is preferably performed using technical means, in particular a computer. In particular, the data processing method is executed by or on the computer. The computer in particular comprises a processor and a memory in order to process the data, in particular electronically and/or optically. The calculating steps described are in particular performed by a computer. Determining or calculating steps are in particular steps of determining data within the framework of the technical data processing method, in particular within the framework of a program. A computer is in particular any kind of data processing device, in particular electronic data processing device. A computer can be a device which is generally thought of as such, for example desktop PCs, notebooks, netbooks, etc., but can also be any programmable apparatus, such as for example a mobile phone or an embedded processor. A computer can in particular comprise a system (network) of “sub-computers”, wherein each sub-computer represents a computer in its own right. The term of computer encompasses a cloud computer, in particular a cloud server. The term of cloud computer encompasses cloud computer system in particular comprises a system of at least one cloud computer, in particular plural operatively interconnected cloud computers such as a server farm. Preferably, the cloud computer is connected to a wide area network such as the world wide web (WWW). Such a cloud computer is located in a so-called cloud of computers which are all connected to the world wide web. Such an infrastructure is used for cloud computing which describes computation, software, data access and storage services that do not require end-user knowledge of physical location and configuration of the computer that delivers a specific service. In particular, the term “cloud” is used as a metaphor for the internet (world wide web). In particular, the cloud provides computing infrastructure as a service (IaaS). The cloud computer may function as a virtual host for an operating system and/or data processing application which is used for executing the inventive method. Preferably, the cloud computer is an elastic compute cloud (EC2) provided by Amazon Web Services™. A computer in particular comprises interfaces in order to receive or output data and/or perform an analogue-to-digital conversion. The data are in particular data which represent physical properties and/or are generated from technical signals. The technical signals are in particular generated by means of (technical) detection devices (such as for example devices for detecting marker devices) and/or (technical) analytical devices (such as for example devices for performing imaging methods), wherein the technical signals are in particular electrical or optical signals. The technical signals represent in particular the data received or outputted by the computer.

Within the framework of the invention, computer program elements can be embodied by hardware and/or software (this includes firmware, resident software, micro-code, etc.). Within the framework of the invention, computer program elements can take the form of a computer program product which can be embodied by a computer-usable, in particular computer-readable data storage medium comprising computer-usable, in particular computer-readable program instructions, “code” or a “computer program” embodied in said data storage medium for use on or in connection with the instruction-executing system. Such a system can be a computer; a computer can be a data processing device comprising means for executing the computer program elements and/or the program in accordance with the invention, in particular a data processing device comprising a digital processor (central processing unit—CPU) which executes the computer program elements and optionally a volatile memory (in particular, a random access memory—RAM) for storing data used for and/or produced by executing the computer program elements. Within the framework of the present invention, a computer-usable, in particular computer-readable data storage medium can be any data storage medium which can include, store, communicate, propagate or transport the program for use on or in connection with the instruction-executing system, apparatus or device. The computer-usable, in particular computer-readable data storage medium can for example be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, apparatus or device or a medium of propagation such as for example the Internet. The computer-usable or computer-readable data storage medium could even for example be paper or another suitable medium onto which the program is printed, since the program could be electronically captured, for example by optically scanning the paper or other suitable medium, and then compiled, interpreted or otherwise processed in a suitable manner. Preferably, the data storage medium is a non-volatile data storage medium. The computer program product and any software and/or hardware described here form the various means for performing the functions of the invention in the example embodiments. The computer and/or data processing device can in particular include a guidance information device which includes means for outputting guidance information. The guidance information can be outputted, for example to a user, visually by a visual indicating means (for example, a monitor and/or a lamp) and/or acoustically by an acoustic indicating means (for example, a loudspeaker and/or a digital speech output device) and/or tactilely by a tactile indicating means (for example, a vibrating element or vibration element incorporated into an instrument).

The invention also relates to a program which, when running on a computer or when loaded onto a computer, causes the computer to perform one or more or all of the method steps described herein and/or to a program storage medium on which the program is stored (in particular in a non-transitory form) and/or to a computer on which the program is running or into the memory of which the program is loaded and/or to a signal wave, in particular a digital signal wave, carrying information which represents the program, in particular the aforementioned program, which in particular comprises code means which are adapted to perform any or all of the method steps described herein.

The present invention is also directed to a navigation system for position determination in particular in the field of computer-assisted surgery. This navigation system preferably comprises the aforementioned computer for processing the data provided in accordance with the data processing method as described in any one of the preceding embodiments, in particular for processing the first and second body part transformation data/information and the reference structure position transformation data/information. The navigation system preferably comprises a detection device for detecting the positions of the first and second reference structures, in order to generate detection signals and to supply the generated detection signals to the computer such that the computer can determine the reference structure position transformation data/information on the basis of the detection signals received. The navigation system also preferably comprises a user interface for receiving the calculation results from the computer. The user interface provides the received data to the user as information, in particular graphical information. Examples of a user interface include a monitor or a loudspeaker. The user interface can use any kind of indication signal (for example a visual signal, an audio signal and/or a vibration signal).

The expression “acquiring data” encompasses in particular (within the framework of a data processing method) the scenario in which the data are determined by the data processing method or program. Determining data in particular encompasses measuring physical quantities and transforming the measured values into in particular digital data and/or computing the data by means of a computer, in particular computing the data within the method of the invention. The meaning of “acquiring data” in particular also encompasses the scenario in which the data are received or retrieved by the data processing method or program, for example from another program, a previous method step or a data storage medium, in particular for further processing by the data processing method or program. Thus, “acquiring data” can also for example mean waiting to receive data and/or receiving the data. The received data can for example be inputted via an interface. “Acquiring data” can also mean that the data processing method or program performs steps in order to (actively) receive or retrieve the data from a data source, for instance a data storage medium (such as for example a ROM, RAM, database, hard disc, etc.) or via the interface (for instance, from another computer or a network). The data can achieve the state of being “ready for use” by performing an additional step before the acquiring step. In accordance with this additional step, the data are generated in order to be acquired. The data are in particular detected or captured (for example, by an analytical device). Alternatively or additionally, the data are inputted in accordance with the additional step, for instance via interfaces. The data generated can in particular be inputted (for instance, into the computer). In accordance with the additional step (which precedes the acquiring step), the data can also be provided by performing the additional step of storing the data in a data storage medium (such as for example a ROM, RAM, CD and/or hard drive), such that they are ready for use within the framework of the method or program in accordance with the invention. Thus, “acquiring data” can also involve commanding a device to obtain and/or provide the data to be acquired. The acquiring step in particular does not involve an invasive step which would represent a substantial physical interference with the body requiring professional medical expertise to be carried out and entailing a substantial health risk even when carried out with the required professional care and expertise. Acquiring, in particular determining, data in particular does not involve a surgical step and in particular does not involve a step of treating a human or animal body using surgery or therapy. This also applies in particular to any steps directed to determining data. In order to distinguish the different data used by the present method, the data are denoted (i.e. referred to) as “XY data” and the like and are defined by the information which they describe which is preferably called “XY information”.

Where in the framework of this disclosure it is mentioned that data comprise a certain information, the respective data in particular or consists of the respective information. Where in the framework of this disclosure it is mentioned that information describes a specific information content, the information may also be or consist of the respective information content rather than just describing the information content as a kind of metadata.

Preferably, the inventive method is at least partly executed by a computer. That is, all steps or just some of the steps (i.e. less than a total number of steps) of the inventive method may be executed by a computer.

In the following, example embodiments of the present invention are described with reference to the Figures, which are merely to be regarded as examples of the invention without limiting the invention to the specific embodiment, wherein FIGS. 1 to 7 illustrate the first embodiment inventive method of acquiring contact position parameters of two body parts which are connected to each other by a joint (to acquire a kinematic footprint), and FIGS. 8 to 16 illustrate the method to detect contact between components of a joint (making use of a CJM) whereas FIG. 17 gives an overview over all used methods and their relations:

FIG. 1 illustrates the general setup for determining the joint position transformation;

FIGS. 2 a and 2 b describe the working principle of acquiring the range of motion of an artificial knee joint;

FIGS. 3 a and 3 b illustrate the definition of used transformations;

FIGS. 4 a and 4 b illustrate a sequence of shifts and rotations resulting from decomposition of the joint position transformation;

FIG. 5 illustrates a grid of position parameters by showing a 3D-subgrid of the 4D-grid of nodes for an arbitrary given value of flex=0;

FIG. 6 illustrates a tree structure including some example nodes of the position parameter grid;

FIG. 7 illustrates the structure of a text file storing the grid as lines of data per node;

FIGS. 8 a and 8 b illustrate a joint position transformation describing a contact position and a position in which no contact is established, respectively;

FIG. 9 illustrates finding contact position parameters based on application of a continuous joint model of giving values of ml, ap, ie and flex;

FIG. 10 illustrates a visualized pose of the artificial knee joint and a matrix representing the corresponding joint position transformation;

FIG. 11 illustrates feeding the position parameters determined from the matrix of FIG. 10 into a continuous joint model to establish model values for pd and vv;

FIGS. 12 a and 12 b illustrate a contact position generated based on the modeled values for the modeled free parameters pd and vv;

FIGS. 13 a and 13 b illustrate an angular deviation between the tracked pose and the contact position determined based on the continuous joint model;

FIG. 14 illustrates proposed contact locations for a situation of no contact in a knee joint comprising the artificial knee joint, computed and visualized by a prio-art computer application that does not make use of the second embodiment of the inventive method and thus fails to detect that no contact occurs;

FIG. 15 illustrates an indication of wrong contact locations detected by the prior-art application used for generating the visualization of FIG. 14.

FIG. 16 shows a postoperative movement state after inserting implant components into femur and tibia as starting point to apply the second embodiment of the inventive method to detect contact between components of a joint.

FIG. 17 shows the relations between the first and second embodiment of the inventive methods and the CJM; the first embodiment of the inventive method of acquiring contact position parameters of two body parts which are connected to each other by a joint (kinematic footprint, on the left) provides contact position datasets, these datasets are used in the method of determining contact position parameters of a joint connecting two bones to establish a CJM (in the middle), A CJM in turn is used in the second embodiment of the inventive method to detect contact between components of a joint (on the right).

Note that figures illustrating the CJM and the method of determining contact position parameters of a joint connecting two bones are not contained here but disclosed in the applicant's co-pending patent application PCT/EP2011/072323 having the title “Method of determining contact position parameters of a joint connecting two bones” and the attorney's reference 58420 XX which was filed on Dec. 9, 2011, the entire contents of which being incorporated into this application by reference.

The features described with reference to FIGS. 1 to 7 in particular serve to determine a kinematic implant footprint by using in particular a tracking system. The kinematic implant footprint represents a kinematic characteristic of the implant components 1, 2. The data received thereby is preferably utilized to feed a continuous joint model CJM which relies on such discrete kinematic data to model implant kinematics in continuous parameter space. For example, a CJM can be used to animate and graphically represent a continuous implant bending movement or other custom ranges of motion.

FIG. 1 shows the general setup for determining the joint position transformation J by moving a first reference structure embodied by reference star 5 (comprising three markers 7) attached via a marker holder 3 to a first body part embodied by a femur component 1 of an artificial knee joint by action of a user's hand 15. Further shown is a navigation system 21 comprising a stereotactic camera 9 for tracking the markers 7. The stereotactic camera 9 is operatively coupled to a computer 10 comprising a non-volatile memory embodied by a hard disc 11, a volatile memory embodied by a RAM 12 and a processor embodied by CPU 13. The computer 10 is also operatively coupled to a visual indicating means embodied by monitor 14.

As shown by FIGS. 2 a and 2 b, the reference star 5 is manually moved relative to a second reference structure embodied by a reference star 6 comprising three markers 8. The reference star 6 is fixed, via marker holder 4, to a second body part embodied by a tibia component 2 of an artificial knee joint. Preferably, a rack part 4′ for attaching the marker holder 4 mounted to the tibia component 2 with a predetermined spatial relationship, e.g. parallel to a sagittal and a frontal plane of the artificial knee joint. During the relative movement of the reference star 5 and reference star 6, both reference stars 5, 6 have a fixed position relative to the femur component 1 and the tibia component 2, respectively. According to FIG. 2 a which represents a section through a sagittal plane of the artificial knee joint, the relative movement of the reference stars 5, 6 takes place in a proximodistal (pd) direction, an anterioposterior (ap) direction and around a flexion/extension rotation (flex) of the artificial knee joint. According to FIG. 2 b, the reference stars 5, 6 are also moved relative to each other by moving the reference star 5 and the femur component 1, respectively, around a varus-valgus (vv) rotation, and along shifts in a mediolateral (ml) direction and around an internal/external (ie) rotation of the artificial knee joint. This allows for measurement of contact position parameters describing six degrees of freedom of the artificial knee joint while a user may assure contact between the femur component 1 and the tibia component 2 by manual pressure with his hand 15.

The process described with reference to FIGS. 1 and 2 can also be summarized as follows. The variation of the pose is achieved by an operator who shifts and rotates the components of the artificial joint with respect to each other. The resulting sequence of implant component poses is acquired with the tracking system (e.g. camera-based). Alternatively, some sort of driven device may be used to move the components automatically and systematically. Most importantly, stable contact must be established between the component surfaces at all times during execution of the tracking and/or movement of the joint components. According to FIGS. 1, 2 a and 2 b, the tibia implant component 2 can be fixed in a rack comprising the marker holder 4 and its rack part 4′. The tibia component can comprise only a tibia insert alone or a tibia tray with an insert mounted to it. Reference stars 5, 6 with markers 7, 8 are attached to both joint components 1, 2 and tracked throughout the acquisition process. The operator varies a dedicated degree of freedom of for example the femur component 1. For a first run, he would most conveniently adjust the target values of flex and ie to some value (e.g. flex=0, ie=0) and keep them fixed while shifting the femur component 1 in the ap and ml direction across the surface of the tibia component 2. Preferably, the operator pursues steady and stable two-point contact between the femur component 1 and the tibia component 2. Hence, the varus-valgus angle vv and the proximodistal shift pd of the femur component 1 are being intuitively adapted by the operator according to the component shape using his tactile sense when pressing the femur component onto the tibial component. In a series of subsequent runs, the operator would change the ie rotation and the flex rotation in steps to cover the whole feasible range of motion for the pair of joint components 1, 2. During each run, the tracking system steadily determines a reference structure position transformation S between the reference star 5 of the femur component 1 and the reference star 6 of the tibia component 2.

With reference to FIG. 3 a, a reference structure position transformation S is determined between a coordinate system 16 which rests relative to the reference star 5 and a coordinate system 17 which rests relative to the reference star 6. The first body part position transformation F between a coordinate system 18 resting relative to the femur component 1 and a coordinate system 16 resting relative to the reference star 5 is preferably predetermined and acquired for example by using a coordinate measuring machine. In analogy, the second body part position transformation T between a coordinate system 19 resting relative to the tibia component 2 and a coordinate system 17 resting relative to the reference star 6 is shown in FIG. 3 b also preferably predetermined and known. The reference structure position transformation S is preferably steadily (i.e. at consecutive discrete points in time) determined during the relative movement of the reference stars 5 and 6. Based on the knowledge of F, S and T, the joint position transformation J is determined from the equation J=T⁻¹·S·F. The joint position transformation J is a transformation between the coordinate system 18 resting relative to the femur component 1 and the coordinate system 19 resting relative to the tibia component 2.

FIGS. 4 a and 4 b give a visual impression of a decomposition of the matrix representing the joint position transformation J into its six basic parameters pd, ap, ml, ie, vv and fe (flex). The transformation J between the coordinate system 18 of the femur component 1 (COSF) and the coordinate system 19 of the tibia component 2 (COST) can be described as a sequence of shifts (translations) ml, ap, pd and rotations vv, ie and flex (preferably, all in this order). The decomposition of transformation J into its parameters is also termed parameter extraction. The parameters correspond to the rotations and shifts applied by the user.

The shifts ml (in x-direction of the tibia coordinate system 19), ap (in y-direction of the tibia coordinate system 19) and pd (in z-direction of the tibia coordinate system 19) correspond to the elements of the component pose transformation J a follows:

-   -   Ml=J₁₄     -   ap=J₂₄     -   pd=J₃₄

The rotations follow the sequence vv (1. around the y-direction of the femur coordinate system 18), ie (2. around the z-direction of the femur coordinate system 18), flex (3. around the x-direction of the femur coordinate system 18). At the beginning of the rotation sequence, the femur implant coordinate system (COSF) 18 is aligned with the tibia coordinate system (COST) 19. The first step is a rotation of COSF around the y-axis of COST by an angle vv. As a result, COSF changes its orientation. The next step is a rotation of COSF around its moved z-axis by an angle ie. The last step of a rotation of COSF around its new x-axis by an angle flex. The second and third rotations are applied to coordinate axes moved by a subsequent rotation. From the elements of J, the rotations can be derived as follows:

-   -   ie=arcsin(J₂₁)     -   flex=arcos(J₂₂/cos(ie)) for J₂₃<0, flex=−arccos(J₂₂/cos(ie)) for         J₂₃>=0     -   vv=−arcsin(J₃₁/cos(ie))

The derived parameters ml, ap, ie, pd, flex and vv give a complete and equivalent description of the component's pose given by J. The angles ie, flex and vv in the formulas above apply in radians.

A specific pose of the artificial knee joint defined by a joint position transformation J and acquired based on tracking the relative position of the reference stars 5, 6 is only considered for the first embodiment of the inventive method if it fits into a predefined 4D-grid of position parameter values. Each node of the grid defines target values for ml, ap, ie and flex. These parameters correspond to the independent shifts and rotations which the operator applies to in particular the femur component 1. The associated parameters vv and pd (i.e. the aforementioned free position parameters) are stored as a pair of dependent attribute values for each grid node, since they result from the kinematic characteristics of the femur component 1 and the tibia component 2 and the adjustment of the independent parameter values. All six parameters of the node represent the component pose which is associated with that node. All nodes of the grid form a discrete representation of the acquired artificial joint kinematics. To fill the grid with data, position parameters for the poses measured during the relative movement of the reference stars 5, 6 are extracted and compared with all the parameter sets describing a specific node. A distance to any node is calculated based on the values for the parameters ie, flex, ap and ml. If the distance to a node is below the given limit, vv and pd will be assigned to that node. If another pose subsequently comes closer in distance to a node, its respective vv and pd values will replace the former values. Calculation of a distance from a node is achieved by e.g. applying Minkowski distance functions. The grid of FIG. 5 is a visualization of a 3D-subgrid constructed at flex=0 (denoting a flexion rotation of 0). Each discrete value plane intersection in the grid represents a node of the 3D-subgrid. The ball depicted in FIG. 5 visualizes an example limit (1 mm/1°) of allowed deviation for the position parameter ml (see lateral shift), ap (see anterior shift) and ie (see internal rotation) around some example node.

FIG. 6 shows the grid represented as a tree structure including some example nodes with values vv and pd and a node number #. Step width for shifts here is 5 mm, step width for angles is 30° (equivalent to 0.524 radians). These step widths are only examples. Practical values especially for angles would be selected much smaller. At the physical limits of possible joint poses, the grid is not filled with values and void nodes exist, for example when shifting the femoral component beyond the physical border of the tibia component in anteposterior direction.

As shown in FIG. 7, the complete grid can be stored in a text file as lines of data per node (in FIG. 7 line numbers represent node numbers). Each line contains the parameter values for a specific node defined by the line number (node number). The step width of the grid has a great influence on data volume and precision. For shifts such as ml and ap, a default step width of 5 mm may be defined. For rotation such as flex and ie, a step width of 5 degrees may be defined as default. With finer widths, the amount of acquired data expands and the accuracy of the resulting continuous joint model (CJM) is improved. But even for larger step widths of e.g. 5 mm and 10°, sub-millimeter accuracy is achieved for pd using the CJM.

During the process of acquiring the stream of poses of the artificial knee joint during the relative movement of the reference stars 5 and 6 which represents a kinematical footprint of the component pair (comprising the femur component 1 and the tibia component 2), the operator is supported to hit all required joint poses in an efficient way. The navigation system provides guidance data and preferably aids him in the acquisition of poses by:

-   -   systematically varying the target values (i.e. the values for         flex and ie) for the next run;     -   showing the deviation to the target values (for ie, flex) during         each run to help the user to stay close to these predefined         target values;     -   showing uncovered nodes (compliant in ie and flex) close to the         current pose and inidicate directions to uncovered nodes in ap         and ml;     -   showing regions of poor coverage in ap and ml during each run.

A systematic variation and display of the target values for specific parameters, e.g. flex and ie, helps the operator to adjust the pose accordingly and reach high coverage in each run. In order to keep on track while moving the femur component 1, the deviation from the target values is also shown. The distance of the current pose enclose uncovered nodes as shown to help the operator approaching yet uncovered nodes. The distance may be decomposed into components in ap and ml direction. Areas of poor coverage are indicated for the operator to guide him to these areas in particular by issuing guidance information which describes a desired direction of movement of the implant components 1, 2 relative to one another.

The following FIGS. 8 to 16 relate to the second embodiment of the inventive method that serves the purpose of detecting contact between two body parts. Once a continuous joint model (CJM) has been established and contains a database of sample contact position datasets, it can be used to detect contact between the components of a particular joint, for example an artificial joint comprising a femur and a tibial component.

The illustrated application example starts with a postoperative movement state after inserting implant components into femur and tibia as shown in FIG. 16. As already explained, the joint position transformation J (see FIG. 16) between the body parts of femur and the tibia component can be derived for example based on medical image data or position data acquired by an imaging apparatus or a navigation system in a post-operative state of the joint. For this example it is assumed that the pose J in FIG. 16 is known and was acquired from tracking data and that it is not known beforehand if the components are in a desired contact and touch at two points or have an undesired one-point contact or no contact at all. By applying the contact detection method this question shall be answered.

FIG. 8 a depicts a position of desired contact between the femur component 1 and the tibia component 2, defined by in particular the joint position transformation J determined for the joint pose shown in FIG. 8 a. In contrast thereto, FIG. 8 b shows the situation in which the joint position transformation J describes a position in which no contact is established between the femur component 1 and the tibia component 2.

FIG. 9 shows the principle of feeding the values for ap, ml, ie, and flex determined based on the decomposition of the joint position transformation J into a CJM for determining modeled values for pd and vv (in the following also denoted as pd_(CJM) and vv_(CJM)). The modeled parameters pd_(CJM) and vv_(CJM) will most likely deviate from pd and vv found by decomposition of the matrix J. The (modeled) values for the modeled parameters pd_(CJM) and vv_(CJM) guarantee contact since the CJM is designed to compute (modeled) values for modeled parameters pd_(CJM) and vv_(CJM) which describe a contact position. The measured values for pd and vv found by decomposition of the matrix stem from the actual artificial joint under test in a specific pose.

Only if the measured position parameters are close enough to their (modeled) contact counterparts, the transformation J determined by measuring the relative movement of the reference stars 5 and 6 (or the femur component 1 and the tibia component 2, respectively) describes a situation in which the desired contact is established.

FIG. 10 shows the situation of an artificial knee joint in which no contact (i.e. at least no desired contact) is established. The transformation between the coordinate system 18 resting relative to the femur component 1 (the femur coordinate system) and the coordinate system 19 resting relative to the tibia component 2 (the tibia coordinate system) is then described by an exemplary matrix J as illustrated in FIG. 10. Decomposition of this matrix J yields the following parameters: ml=0; ap=0; ie=0; flex=0.524; pd=33.86; vv=0.2.

FIG. 11 now illustrates how these measured parameter values (in particular for ap, ml, fe and ie) received from the decomposition are fed into the continuous joint model in order to establish modeled values for pd_(CJM) and vv_(CJM) which would resemble a contact position.

The pose resulting from these models values is shown in FIGS. 12 a (in a section through a transverse plane of the artificial knee joint) and 12 b (in a section through a frontal plane of the artificial knee joint). The modeled value amount to pd_(CJM)=33.86 and vv_(CJM)=0.0. According to FIGS. 12 a and 12 b, these values resemble a contact position in which the desired contact is established between the femur component 1 and the tibia component 2.

FIGS. 13 a and 13 b show the principle of using a predetermined limit (also termed threshold) for determining the deviation between the measured parameters determined by tracking the movement of the joint components 1, 2 (as described with reference to FIGS. 1, 2 a and 2 b) and the modeled parameters. In the case shown, the deviation is characterized by a deviation of the measured rotation parameter vv from the modeled rotation parameter vv_(CJM) by 0.2 radians equivalent to 11.5°. Note that FIG. 13 a illustrates the pose of the artificial knee joint determined based on the measured parameters, whereas FIG. 13 b shows the pose determined from the modeled parameters and thus illustrates a desired pose. Furthermore, in the shown case, the values for pd and pd_(CJM) are equal and thus no deviation can be determined for this pair of measured and modeled parameters. For a threshold of e.g. 0.5 mm for the deviation of pd and 0.5° for the deviation of vv from their respective modeled counterparts, there clearly does not exist a contact position.

Since the deviation is not within the threshold, it is found that no contact applies in the movement state shown in FIG. 16 and according contact condition information is indicated to the operator by the computer system. Would the deviation have been within the predefined threshold range, a contact would have been indicated to the operator.

FIGS. 14 and 15 show screenshots generated by a prior art computer application for determining a contact position between the tibia component and the femur component when implanted into the tibia and femur, respectively.

FIG. 14 shows a prior art technique in which contact locations in a postoperative range of motion between the femur component 1 and the tibia component 2 are determined based on a simplified search for contact of the femur component 1 with a boundless flat plane. The boundless plane replaces the complex shaped tibia component 2 to simplify the search for contact points. The prior art technique referred to searches the deepest points in the femoral three-dimensional model in direction of the plane's normal vector. Since this approach simplifies the problem of finding contact points considerably, drawbacks occur: One limitation of such a technique is that contact may be detected when there actually is no contact, e.g. because the femur component 1 is shifted apart from the tibia component 2 in the pd-direction or contact is lost at the second contact location due to a vv-rotation. Thus, despite the fact that there actually is no contact, contact locations are calculated and shown. FIG. 15 shows a further weakness of this prior art technique, namely that contact between the femur component 1 and the tibia component 2 may be wrongly detected outside the actual physical boundaries of the tibia component 2.

Applying the contact detection method presented herein, this prior art's limitation can be overcome. In order to avoid the wrong detection of contact points for a position in which actually no contact exists, the aforementioned method features may be included in the computer application to improve it such that contact positions of the femur component 1 and the tibia component 2 are verified by using the proposed method to detect contact between components of a joint. For example, for any pose to be visualized it will be checked whether it is a contact position, before the contact points are actually determined, in particular calculated. Thereby, showing contact points for torn apart joint components will be avoided (in contrary to FIG. 14). Contact points found outside the physically possible boundaries will also be masked out (in contrary to FIG. 15).

The relations of the different methods is shown in FIG. 17. The first embodiment of the inventive method of acquiring contact position parameters of two body parts which are connected to each other by a joint (kinematic footprint) provides contact position datasets for the method of determining contact position parameters of a joint connecting two bones to establish a CJM. The second embodiment of the inventive method to detect contact between components of a joint makes use of a CJM. 

1. A data processing method of determining a transformation for the relative positions of two body parts which are connected to each other by a joint, the method comprising the following steps: a) acquiring first body part position transformation data comprising first body part position transformation information describing a first body part position transformation for the position of a first body part of the two body parts relative to a first reference structure assigned to the first body part; b) acquiring second body part position transformation data comprising second body part position transformation information describing a second body part position transformation for the position of a second other body part of the two body parts relative to a second other reference structure assigned to the second body part; c) acquiring reference structure position transformation data comprising reference structure position transformation information describing a reference structure position transformation for the position of the first reference structure relative to the second reference structure for at least two movement states of the joint; d) determining, based on the first body part position transformation data and the second body part position transformation data and the reference structure position transformation data, joint position transformation data comprising joint position transformation information describing a joint position transformation for the position of the first body part relative to the second body part for the at least two movement states; and e) determining, based on the joint position transformation data, contact condition data comprising contact condition information describing whether the joint position transformation represents a position of the first and second body parts which is close or is not close to a contact position, wherein the contact position data is determined based on acquiring a data set of parameters including: a mediolateral (ml) parameter, an anterioposterior (ap) parameter, a proximodistal (pd) parameter, internal/external rotation (ie) angle parameter, a flexion angle parameter, and a varus-valgus (vv) angle parameter, wherein the data set of parameters describes the joint position transformation information, decomposing the joint position transformation based on acquiring a subset of n of the parameters that includes at least one of the ml parameter, the ap parameter, the pd parameter, and the flex parameter as an input parameter data set, wherein n is an integer in a range of one to five describing a number of predetermined parameters, determining modelled 6-n free parameters based on proximodistal modelled values and varus-valgus modelled values of the joint position transformation information and determining a model joint position transformation based on changing the joint position transformation information according to the modelled 6-n free parameters; wherein the contact position data is determined further based on determining whether a deviation of measured values for the 6-n free parameters is within a predetermined limit from the modelled values of the modelled 6-n free parameters and on determining that the joint position transformation describes a contact position of the first and second body parts if the deviation is within the predetermined limit.
 2. The method according to claim 1, wherein the first reference structure has a predetermined position relative to the first body part, and wherein the second reference structure has a predetermined position relative to the second body part.
 3. The method according to claim 1, wherein step c) comprises moving first and second body parts relative to one another.
 4. The method according to claim 3, wherein at least one of the first and second body parts is moved manually or by a driving unit.
 5. The method according to claim 1, wherein the joint is an artificial knee joint, the first body part is the femur component of the artificial knee joint, and the second body part is the tibia component of the artificial knee joint.
 6. The method according to claim 1, wherein determining the joint position transformation data comprises determining position parameters comprising at least one rotation parameter and at least one translation parameter between the coordinate system that is assigned to the first body part and the coordinate system that is assigned to the second body part.
 7. The method according to claim 6, wherein the first body part and the second body part are in physical contact with one another in each of the at least two movement states and wherein contact position transformation data is determined comprising contact position transformation information.
 8. The method according to claim 7, comprising: acquiring position parameter grid data comprising position parameter grid information describing a grid of the position parameters for at least four degrees of freedom, wherein the nodes of the grid represent independent translations and/or independent rotations of the joint position transformation; acquiring node assignment condition data comprising node assignment condition information describing at least one condition for the at least one determined position parameters to be fulfilled for assigning the determined at least one position parameters to a node of the grid; determining, based on the position parameter grid data and the node assignment condition data, whether the at least one determined position parameters fulfil a condition to be assigned to the node, and if they fulfil the condition, assigning the at least one determined position parameters to that node.
 9. The method according to claim 7, wherein if the at least one determined position parameters are assigned to a node, it is determined that the movement stage of the joint in which the position parameters were determined includes a contact position.
 10. (canceled)
 11. (canceled)
 12. The method according to claim 1 comprising outputting guidance data comprising guidance information to an operator which describes a desired direction of movement of the first and second body parts relative to one another, wherein the first body part and the second body part are in physical contact with one another in each of the at least two movement states and wherein contact position transformation data is determined comprising contact position transformation information.
 13. A computer program which, when running on a computer or when loaded onto a computer, causes the computer to digital a) acquire first body part position transformation data comprising first body part position transformation information describing a first body part position transformation for the position of a first body part of the two body parts relative to a first reference structure assigned to the first body part; b) acquire second body part position transformation data comprising second body part position transformation information describing a second body part position transformation for the position of a second other body part of the two body parts relative to a second other reference structure assigned to the second body part; c) acquire reference structure position transformation data comprising reference structure position transformation information describing a reference structure position transformation for the position of the first reference structure relative to the second reference structure for at least two movement states of the joint; d) determine, based on the first body part position transformation data and the second body part position transformation data and the reference structure position transformation data, joint position transformation data comprising joint position transformation information describing a joint position transformation for the position of the first body part relative to the second body part for the at least two movement states; and e) determine, based on the joint position transformation data, contact condition data comprising contact condition information describing whether the joint position transformation represents a position of the first and second body parts which is close or is not close to a contact position, wherein the contact position data is determined based on acquiring a data set of parameters including: a mediolateral (ml) parameter, an anterioposterior (ap) parameter, a proximodistal (pd) parameter, internal/external rotation (ie) angle parameter, a flexion angle parameter, and a varus-valgus (vv) angle parameter, wherein the data set of parameters describes the joint position transformation information, decomposing the joint position transformation based on acquiring a subset n of the parameters that includes at least one of the ml parameter, the ap parameter, the pd parameter, and the flex parameter as an input parameter data set, wherein n is an integer in a range of one to five describing a number of predetermined parameters, determining modelled 6-n free parameters based on proximodistal modelled values and varus-valgus modelled values of the joint position transformation information and determining a model joint position transformation based on changing the joint position transformation information according to the modelled 6-n free parameters; wherein the contact position data is determined further based on determining whether a deviation of measured values for the 6-n free parameters is within a predetermined limit from the modelled values of the modelled 6-n free parameters and on determining that the joint position transformation describes a contact position of the first and second body parts if the deviation is within the predetermined limit.
 14. A navigation system for computer-assisted surgery, comprising: a computer executing the computer program of claim 13, for processing the first body part position transformation data, the second body part position transformation data and the reference structure position transformation data; a detection device for detecting the position of the first and second reference structures; a data interface for receiving data comprising information describing the position of the first and second reference structure and for supplying that data to the computer; and a user interface for receiving data from the computer in order to provide information to a user, wherein the received data are generated by the computer on the basis of the results of the processing performed by the computer. 